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Trigonomteric Functions: Problem Solving Approach

by: A. Panchishkin, E. Shavgulidze

Topics: equations, functions, graphs, identities, inequalities, limits, problems and solutions, radians, trigonometry

Collection: mir-titles; additional_collections

Language: English

The back cover says:

This study aid is to help the student to master the basic techniques of solving difficult problems in trigonometry. The book contains theoretical material, many worked competition problems, and some problems to be solved independently (the answers being at end of the book.) Intended for high-school and precollege students.

The book has some interesting things, for example it introduces the trigonometric functions as a feature of a trigonometric circle instead of a right-angled triangle as many books do. Also the second chapter (Identical Transformations of Trigonometric Expressions) will help you understand many combination formulae (which we learn by heart in many cases without understanding). Chapter 4 (Investigating Trigonometric Functions) treats the trigonometric functions graphically and analyzes the meaning of graphs, also with help of their derivatives.

The book was translated from the Russian by Leonid Levant and was first published by Mir in 1988.

Contents:

From the Authors
Contents
5
Chapter 1. Definitions and Basic Properties of Trigonometric Functions 9

1.1. Radian Measure of an Arc. Trigonometric Circle 9
1.2. Definitions of the Basic Trigonometric Functions 18
1.3. Basic Properties of Trigonometric Functions 23
1.4. Solving the Simplest Trigonometric Equations. Inverse Trigonometric Functions 31
Problems 36

Chapter 2. Identical Transformations of Trigonometric Expressions 41

2.1. Addition Formulas 41
2.2. Trigonometric Identities for .Double, Triple, and Half Arguments 55
2.3. Solution of Problems Involving Trigonometric Transformations 63
Problems 77

Chapter 3. Trigonometric Equations and Systems of Equations 80

3. 1. General 80
3.2. Principal Methods of Solving Trigonometric Equations 87
3.3. Solving Trigonometric Equations and Systems of Equations in Several Unknowns 101
Problems 109

Chapter 4. Investigating Trigonometric Functions 113

4.1. Graphs of Basic Trigonometric Functions 113
4.2. Computing Limits 126
4.3. Investigating Trigonometric Functions with the Aid of a Derivative 132
Problems 146

Chapter 5. Trigonometric Inequalities 149

5.1. Proving Inequalities Involving Trigonometric Functions 149
5.2. Solving Trigonometric Inequalities 156
Problems 162
Answers 163